Question

If $A = \begin {bmatrix} \alpha & 0 \\\ 1 & 1 \end {bmatrix}$ and $B= \begin {bmatrix} 1 & 0 \\\ 5 & 1 \end {bmatrix}$ then value of $\alpha$ for which $A^2=B$ is

• A. 1
• B. 2
• C. 4
• D. no real values

Answer 1

Answer: (D)

no real values

Answer 2

Given, A =A = $\begin {bmatrix} \alpha & 0 \\\ 1 & 1 \end {bmatrix}$ and B= $\begin {bmatrix} 1 & 0 \\\ 5 & 1 \end {bmatrix}$
$\Rightarrow \ \ A^2\begin {bmatrix} \alpha & 0 \\\ 1 & 1 \end {bmatrix} \begin {bmatrix} \alpha & 0 \\\ 1 & 1 \end {bmatrix} = \begin {bmatrix} \alpha^2 & 0 \\\ \alpha+1 & 1 \end {bmatrix}$
Also, given, A$^2$=B
$\Rightarrow \ \ \begin {bmatrix} \alpha^2 & 0 \\\ \alpha+1 & 1 \end {bmatrix} = \begin {bmatrix} 1 & 0 \\\ 5 & 1 \end {bmatrix}$
$\Rightarrow \ \ \alpha^2=1 \ and \ \alpha+1=5$
Which is not possible at the same time.
$\therefore$ No real values of a exists.